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Nonsmooth Methods for Control Design with Integral Quadratic Constraints

Pierre Apkarian(Pierre.Apkarian***at***onera.fr)
Dominikus Noll(dominikus.noll***at***math.univ-toulouse.fr)
Olivier Prot(olivier.prot***at***unilim.fr)

Abstract: We develop an optimization technique to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use the fact that IQCs may be transformed into semi-infinite maximum eigenvalue constraints over the frequency axis and approach them via nonsmooth optimization methods. We develop a suitable spectral bundle method and prove its convergence in the sense that, for an arbitrary starting point, the accumulation points of the sequence of serious iterates are critical. Our new way to look at IQCs is particularly suited for systems with large state dimension, because we avoid the use of Lyapunov variables. We present two numerical tests which validate our approach in the case of parametric uncertainties.

Keywords: Robust control, parametric uncertainty, integral quadratic constraint (IQC), structured controllers, $NP$-hard problems, nonsmooth optimization

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Université Paul Sabatier, Toulouse, France, 2008

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Entry Submitted: 02/24/2015
Entry Accepted: 02/24/2015
Entry Last Modified: 02/24/2015

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